Israel insists Hamas must no longer be able to smuggle in weapons through tunnels under the Gaza-Egypt border, and must end its rocket attacks on its southern towns.
The office of Ehud Olmert, the Israeli prime minister, said Condoleezza Rice, the US secretary of state, told him "the United States would be prepared to assist in solving the issue of smuggling".
Israeli leaders were expected to make decisions on the proposal on Thursday, after Israeli envoy Amos Gilad returned from a day-long trip to Cairo where he discussed the issue with Egyptian officials.
Gulf Co-operation Council (GCC) leaders meeting in Riyadh, the Saudi capital, on Thursday to discuss the crisis agreed to continue the deliberations at a summit in Kuwait on Monday.
The Saudi summit came a day after Qatar unveiled its own plan for an Arab League meeting on the war to be held in Doha, the capital of Qatar, on Friday.
"We all know it is shameful to discuss the national and human cost of Gaza that has now been stained with children's blood at the margin of a previously planned summit," Sheikh Hamad bin Khalifa Al Thani, the emir of Qatar, said.
"We have renewed our invitation for an emergency Arab summit in Doha but, whenever quorum has been reached, it falls short again."
When asked about the Doha summit, Saudi officials said there was no quorum to convene it.
But some leaders have arrived in Doha for the summit, including president Bashar al-Assad of Syria and Abdelaziz Bouteflika of Algeria.